Speaking from a londoner point of view - I had 3 cancellations last week (on the 1st day of the strike: 2x 2hr bookings, and a 1hour booking ) pre booked by regulars, and no phonecalls on the second day of the strike whatsoever, and given it was a Thursday- my busiest day in normal circumstances- So yes, i can say definitely my earnings were affected by the strike.
I guess, if you are by a major train station, you should be fine in theory, and even get some extra people who are just killing the time waiting for a train/traffic to ease etc. But if I was you I wouldn't risk it. Also, it's really unpredictable how long a journey is going to take when all you have is buses you can't get on, and taxis that are not moving anywhere! I got stuck in traffic on Wednesday around Paddington area, and it took around 40 mins to move 200yards (!)